1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 Data: The COVID_19 Data-Set

The data to process is described in:

https://zenodo.org/record/4156647#.Y1bSF3bMKUk

IR Saliva Testing Dataset

10.5281/zenodo.4156647 https://doi.org/10.5281/zenodo.4156647

I added a column to the data identifying the repeated experiments.


SalivaIR <- as.data.frame(read_excel("~/GitHub/FCA/Data/SalivaThermal_Source_Data_2.xlsx"))


SalivaIR_set1 <- subset(SalivaIR,RepID==1)
rownames(SalivaIR_set1) <- SalivaIR_set1$ID
SalivaIR_set1$RepID <- NULL
SalivaIR_set1$ID <- NULL
SalivaIR_set1$Ct <- NULL

SalivaIR_set2 <- subset(SalivaIR,RepID==2)
rownames(SalivaIR_set2) <- SalivaIR_set2$ID
SalivaIR_set2$RepID <- NULL
SalivaIR_set2$ID <- NULL
SalivaIR_set2$Ct <- NULL

SalivaIR_set3 <- subset(SalivaIR,RepID==3)
rownames(SalivaIR_set3) <- SalivaIR_set3$ID
SalivaIR_set3$RepID <- NULL
SalivaIR_set3$ID <- NULL
SalivaIR_set3$Ct <- NULL

SalivaIR_Avg <- (SalivaIR_set1 + SalivaIR_set2 + SalivaIR_set3)/3


colnames(SalivaIR_Avg) <- paste("V",colnames(SalivaIR_Avg),sep="_")

SalivaIR_Avg$class <- 1*(str_detect(rownames(SalivaIR_Avg),"P"))

pander::pander(table(SalivaIR_Avg$class))
0 1
30 31

1.2.0.1 Standarize the names for the reporting

studyName <- "IRSaliva"
dataframe <- SalivaIR_Avg
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))
rows col
61 251
pander::pander(table(dataframe[,outcome]))
0 1
30 31

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns


  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.999994

1.5 The decorrelation


DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  V_1138 
#>     V_1300     V_1298     V_1296     V_1294     V_1292     V_1290 
#> 0.03571429 0.04017857 0.05357143 0.05803571 0.06250000 0.06696429 
#> 
#>  Included: 224 , Uni p: 0.0006696429 , Base Size: 1 , Rcrit: 0.4015439 
#> 
#> 
 1 <R=1.000,thr=0.950>, Top: 1< 223 >[Fa= 1 ]( 1 , 223 , 0 ),<|><>Tot Used: 224 , Added: 223 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=0.999,thr=0.950>, Top: 4< 20 >[Fa= 5 ]( 4 , 40 , 1 ),<|><>Tot Used: 224 , Added: 40 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=0.998,thr=0.950>, Top: 11< 20 >[Fa= 16 ]( 11 , 67 , 5 ),<|><>Tot Used: 224 , Added: 67 , Zero Std: 0 , Max Cor: 1.000
#> 
 4 <R=0.992,thr=0.950>, Top: 20< 3 >[Fa= 36 ]( 20 , 52 , 16 ),<|><>Tot Used: 224 , Added: 52 , Zero Std: 0 , Max Cor: 1.000
#> 
 5 <R=0.978,thr=0.950>, Top: 19< 19 >[Fa= 55 ]( 19 , 68 , 36 ),<|><>Tot Used: 224 , Added: 68 , Zero Std: 0 , Max Cor: 1.000
#> 
 6 <R=0.971,thr=0.950>, Top: 20< 28 >[Fa= 75 ]( 20 , 91 , 55 ),<|><>Tot Used: 224 , Added: 91 , Zero Std: 0 , Max Cor: 0.999
#> 
 7 <R=0.961,thr=0.950>, Top: 22< 5 >[Fa= 97 ]( 22 , 55 , 75 ),<|><>Tot Used: 224 , Added: 55 , Zero Std: 0 , Max Cor: 0.999
#> 
 8 <R=0.947,thr=0.950>, Top: 19< 3 >[Fa= 116 ]( 19 , 36 , 97 ),<|><>Tot Used: 224 , Added: 36 , Zero Std: 0 , Max Cor: 0.998
#> 
 9 <R=0.932,thr=0.950>, Top: 11< 2 >[Fa= 127 ]( 11 , 18 , 116 ),<|><>Tot Used: 224 , Added: 18 , Zero Std: 0 , Max Cor: 0.998
#> 
 10 <R=0.924,thr=0.950>, Top: 8< 1 >[Fa= 135 ]( 8 , 10 , 127 ),<|><>Tot Used: 224 , Added: 10 , Zero Std: 0 , Max Cor: 0.988
#> 
 11 <R=0.918,thr=0.950>, Top: 1< 1 >[Fa= 136 ]( 1 , 1 , 135 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.950
#> 
 12 <R=0.917,thr=0.900>, Top: 49< 1 >[Fa= 138 ]( 49 , 54 , 136 ),<|><>Tot Used: 224 , Added: 54 , Zero Std: 0 , Max Cor: 0.997
#> 
 13 <R=0.926,thr=0.950>, Top: 30< 1 >[Fa= 147 ]( 30 , 31 , 138 ),<|><>Tot Used: 224 , Added: 31 , Zero Std: 0 , Max Cor: 0.995
#> 
 14 <R=0.903,thr=0.950>, Top: 12< 1 >[Fa= 151 ]( 12 , 12 , 147 ),<|><>Tot Used: 224 , Added: 12 , Zero Std: 0 , Max Cor: 0.996
#> 
 15 <R=0.889,thr=0.950>, Top: 2< 1 >[Fa= 151 ]( 2 , 2 , 151 ),<|><>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.950
#> 
 16 <R=0.884,thr=0.900>, Top: 19< 1 >[Fa= 151 ]( 18 , 19 , 151 ),<|><>Tot Used: 224 , Added: 19 , Zero Std: 0 , Max Cor: 0.998
#> 
 17 <R=0.885,thr=0.950>, Top: 9< 1 >[Fa= 153 ]( 9 , 9 , 151 ),<|><>Tot Used: 224 , Added: 9 , Zero Std: 0 , Max Cor: 0.994
#> 
 18 <R=0.879,thr=0.950>, Top: 3< 1 >[Fa= 154 ]( 3 , 3 , 153 ),<|><>Tot Used: 224 , Added: 3 , Zero Std: 0 , Max Cor: 0.949
#> 
 19 <R=0.872,thr=0.900>, Top: 10< 1 >[Fa= 154 ]( 10 , 10 , 154 ),<|><>Tot Used: 224 , Added: 10 , Zero Std: 0 , Max Cor: 0.997
#> 
 20 <R=0.868,thr=0.950>, Top: 4< 1 >[Fa= 154 ]( 4 , 4 , 154 ),<|><>Tot Used: 224 , Added: 4 , Zero Std: 0 , Max Cor: 0.986
#> 
 21 <R=0.860,thr=0.950>, Top: 1< 1 >[Fa= 155 ]( 1 , 1 , 154 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.914
#> 
 22 <R=0.856,thr=0.900>, Top: 1< 1 >[Fa= 156 ]( 1 , 1 , 155 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#> 
 23 <R=0.855,thr=0.800>, Top: 36< 3 >[Fa= 157 ]( 32 , 40 , 156 ),<|><>Tot Used: 224 , Added: 40 , Zero Std: 0 , Max Cor: 0.983
#> 
 24 <R=0.876,thr=0.950>, Top: 6< 1 >[Fa= 157 ]( 6 , 6 , 157 ),<|><>Tot Used: 224 , Added: 6 , Zero Std: 0 , Max Cor: 0.975
#> 
 25 <R=0.863,thr=0.950>, Top: 3< 1 >[Fa= 158 ]( 3 , 3 , 157 ),<|><>Tot Used: 224 , Added: 3 , Zero Std: 0 , Max Cor: 0.938
#> 
 26 <R=0.847,thr=0.900>, Top: 1< 1 >[Fa= 158 ]( 1 , 1 , 158 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.888
#> 
 27 <R=0.842,thr=0.800>, Top: 20< 1 >[Fa= 159 ]( 19 , 20 , 158 ),<|><>Tot Used: 224 , Added: 20 , Zero Std: 0 , Max Cor: 0.953
#> 
 28 <R=0.902,thr=0.950>, Top: 2< 1 >[Fa= 160 ]( 2 , 2 , 159 ),<|><>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.991
#> 
 29 <R=0.896,thr=0.950>, Top: 1< 1 >[Fa= 160 ]( 1 , 1 , 160 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.922
#> 
 30 <R=0.880,thr=0.900>, Top: 3< 1 >[Fa= 160 ]( 3 , 3 , 160 ),<|><>Tot Used: 224 , Added: 3 , Zero Std: 0 , Max Cor: 0.926
#> 
 31 <R=0.870,thr=0.900>, Top: 1< 1 >[Fa= 160 ]( 1 , 1 , 160 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.910
#> 
 32 <R=0.870,thr=0.900>, Top: 1< 1 >[Fa= 160 ]( 1 , 1 , 160 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.885
#> 
 33 <R=0.858,thr=0.800>, Top: 7< 1 >[Fa= 162 ]( 7 , 7 , 160 ),<|><>Tot Used: 224 , Added: 7 , Zero Std: 0 , Max Cor: 0.910
#> 
 34 <R=0.910,thr=0.900>, Top: 1< 1 >[Fa= 162 ]( 1 , 1 , 162 ),<|><>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.799
#> 
 35 <R=0.799,thr=0.800>
#> 
 [ 35 ], 0.7992318 Decor Dimension: 224 Nused: 224 . Cor to Base: 223 , ABase: 224 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

5.5

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

0.036

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

5.08

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.886


varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))
La_V_1124 La_V_856 La_V_964 La_V_996 La_V_1134 La_V_1236
9.48e-10 8.77e-10 5.99e-10 4.91e-10 3.91e-10 3.41e-10

1.5.1 The decorrelation matrix


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

1.5.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 224

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 224

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

[1] 131


    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
#      fc <- cluster_optimal(gr)
        fc <- cluster_walktrap (gr,steps=50)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }


pander::pander(clustable)
  Formula Class ResidualVariance Fscore
V_1184 + V_1184 - (0.786)V_1138 1 0.023 10
V_1186 + V_1186 - (1.016)V_1184 + (0.016)V_1138 1 0.000 6
V_1196 + V_1196 - (2.264)V_1192 + (3.465)V_1186 - (2.481)V_1184 + (0.286)V_1182 - (5.59e-03)V_1138 1 0.000 4
V_1182 + (0.986)V_1186 - (1.985)V_1184 + V_1182 - (3.00e-03)V_1138 1 0.000 4
V_1198 + V_1198 - (1.016)V_1196 + (8.05e-03)V_1138 1 0.000 4
V_1200 + V_1200 - (1.980)V_1198 + (0.981)V_1196 - (2.06e-03)V_1138 1 0.000 1
V_1192 + V_1192 - (7.845)V_1186 + (10.847)V_1184 - (3.993)V_1182 - (7.79e-03)V_1138 1 0.000 0
V_1174 + (3.339)V_1186 - (10.376)V_1184 + (9.839)V_1182 - (3.788)V_1178 + V_1174 - (0.013)V_1138 1 0.000 0
V_1172 + (0.169)V_1184 - (1.172)V_1174 + V_1172 - (1.02e-03)V_1138 1 0.000 0
V_1202 + V_1202 - (3.069)V_1200 + (3.160)V_1198 - (1.092)V_1196 + (1.36e-03)V_1138 1 0.000 -1
V_1178 - (3.326)V_1186 + (8.617)V_1184 - (6.291)V_1182 + V_1178 - (2.38e-04)V_1138 1 0.000 -1
V_1140 + V_1140 - (0.988)V_1138 2 0.000 8
V_1136 + (0.930)V_1140 - (1.932)V_1138 + V_1136 2 0.000 6
V_1214 + V_1214 - (6.03e+02)V_1144 + (2.25e+03)V_1142 - (3.21e+03)V_1140 + (2.09e+03)V_1138 - (5.21e+02)V_1136 2 0.011 4
V_1132 + (3.664)V_1142 - (13.181)V_1140 + (17.389)V_1138 - (8.872)V_1136 + V_1132 2 0.000 3
V_1142 + V_1142 - (2.930)V_1140 + (2.890)V_1138 - (0.960)V_1136 2 0.000 2
V_1150 - (2.057)V_1152 + (3.330)V_1150 - (14.917)V_1140 + (23.462)V_1138 - (9.814)V_1136 2 0.000 0
V_1144 + V_1144 - (3.727)V_1142 + (5.324)V_1140 - (3.461)V_1138 + (0.864)V_1136 2 0.000 0
V_1160 + V_1160 - (12.115)V_1152 + (13.718)V_1150 - (7.898)V_1140 + (5.301)V_1138 2 0.000 -1
V_812 - (0.688)V_1138 + V_812 3 0.051 20
V_810 + (2.65e-03)V_1138 - (1.003)V_812 + V_810 3 0.000 6
V_840 + (0.072)V_1138 + V_840 - (1.106)V_812 3 0.006 3
V_808 + (3.30e-04)V_1138 + (0.909)V_812 - (1.909)V_810 + V_808 3 0.000 2
V_836 + (0.012)V_1138 + V_836 - (1.291)V_830 + (0.272)V_812 3 0.000 0
V_830 + (2.40e-03)V_1138 - (0.649)V_840 + (1.296)V_836 - (0.673)V_830 + (0.024)V_812 3 0.000 0
V_824 - (0.012)V_1138 - (0.369)V_840 + V_824 - (0.611)V_812 3 0.000 0
V_826 + (4.55e-03)V_1138 + V_826 - (1.184)V_824 + (0.178)V_812 3 0.000 -1
V_806 - (1.03e-04)V_1138 - (1.064)V_812 + (3.115)V_810 - (3.051)V_808 + V_806 3 0.000 -1
V_1138 NA 4 1.000 223
V_1114 - (0.962)V_1138 + V_1114 - (9.632)V_972 + (9.553)V_970 4 0.002 8
V_1102 + (3.77e-03)V_1138 + (3.844)V_1114 - (4.856)V_1112 + V_1102 4 0.000 3
V_1112 + (0.077)V_1138 - (1.074)V_1114 + V_1112 4 0.000 2
V_1090 - (0.110)V_1138 + (0.328)V_1114 - (1.272)V_1094 + (1.700)V_1090 - (0.651)V_1086 4 0.000 2
V_1110 - (6.52e-03)V_1138 + (0.776)V_1114 - (1.699)V_1112 + V_1110 - (0.070)V_1102 4 0.000 0
V_1094 + (0.525)V_1138 - (1.532)V_1114 + V_1094 4 0.001 0
V_844 + (6.76e-05)V_1138 + V_844 - (1.100)V_840 + (0.094)V_812 5 0.000 18
V_870 - (6.85e-03)V_1138 + V_870 - (1.027)V_844 5 0.002 3
V_852 - (1.92e-03)V_1138 + V_852 - (1.014)V_844 5 0.000 3
V_858 + (2.22e-03)V_1138 + V_858 - (3.861)V_854 + (3.104)V_852 - (0.246)V_844 5 0.000 2
V_882 + (4.10e-03)V_1138 + V_882 - (1.066)V_880 + (0.066)V_844 5 0.000 1
V_880 - (0.022)V_1138 + (1.652)V_972 - (1.639)V_970 + V_880 - (1.292)V_870 + (0.309)V_844 5 0.000 1
V_854 - (2.59e-04)V_1138 + V_854 - (1.200)V_852 + (0.200)V_844 5 0.000 1
V_876 + (4.01e-03)V_1138 + V_876 - (4.539)V_870 + (3.596)V_868 - (0.057)V_844 5 0.000 -1
V_868 + (1.12e-03)V_1138 - (0.936)V_870 + V_868 - (0.068)V_844 5 0.000 -1
V_956 - (0.316)V_1138 + (16.639)V_1026 - (17.256)V_1024 + V_956 6 0.018 27
V_954 + (0.012)V_1138 - (1.010)V_956 + V_954 6 0.000 8
V_902 + (0.042)V_1138 - (0.318)V_956 + V_902 - (0.712)V_894 6 0.001 3
V_934 + (8.69e-03)V_1138 - (0.887)V_956 + (1.148)V_954 - (1.274)V_938 + V_934 6 0.000 2
V_894 + (0.095)V_1138 - (1.079)V_956 + V_894 6 0.007 2
V_932 + (1.11e-03)V_1138 + (0.029)V_956 - (1.032)V_934 + V_932 6 0.000 1

par(op)

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7992318

1.8 U-MAP Visualization of features

1.8.1 The UMAP on Raw Data


  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

V_1300, V_1274, V_1270, V_1260, V_1202 and V_1200

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

1.8.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

La_V_984, La_V_956, La_V_1002, La_V_1068, La_V_1282 and V_1138


  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

1.9 Univariate Analysis

1.9.1 Univariate



univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : V_1064 200 : V_854




univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_V_1064 200 : La_V_854

1.9.2 Final Table


univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
V_908 0.221 0.128 0.261 0.117 0.579 0.596
V_906 0.220 0.127 0.261 0.117 0.585 0.596
V_904 0.220 0.127 0.261 0.117 0.592 0.596
V_892 0.219 0.127 0.261 0.121 0.626 0.596
V_890 0.219 0.127 0.261 0.121 0.616 0.596
V_888 0.219 0.127 0.261 0.122 0.603 0.596
V_912 0.223 0.129 0.263 0.117 0.604 0.595
V_910 0.222 0.128 0.262 0.117 0.587 0.595
V_896 0.220 0.127 0.261 0.120 0.620 0.595
V_894 0.219 0.127 0.261 0.121 0.625 0.595


topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
La_V_1200 -2.21e-05 1.11e-04 -1.44e-04 1.45e-04 0.694 0.776
La_V_1210 -1.03e-04 2.19e-04 -3.72e-04 3.62e-04 0.618 0.775
La_V_1216 -6.36e-04 1.26e-03 -1.73e-03 1.13e-03 0.814 0.774
La_V_992 -1.82e-04 1.06e-03 -7.60e-04 7.93e-04 0.052 0.759
La_V_1004 -2.06e-04 2.11e-03 -1.62e-03 1.69e-03 0.108 0.756
La_V_1274 6.12e-04 8.38e-04 1.33e-03 9.44e-04 0.130 0.749
La_V_886 -9.64e-06 3.19e-05 2.09e-05 5.89e-05 0.510 0.743
La_V_890 1.12e-04 8.46e-04 6.94e-04 5.50e-04 0.828 0.741
La_V_840 3.51e-03 9.94e-03 1.11e-02 6.82e-03 0.786 0.738
La_V_984 -8.54e-03 3.09e-02 1.28e-02 1.54e-02 0.423 0.729

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))
mean total fraction
5.16 223 0.996

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])
  DecorFormula caseMean caseStd controlMean controlStd controlKSP ROCAUC RAWAUC fscores varratio
La_V_1200 + V_1200 - (1.980)V_1198 + (0.981)V_1196 - (2.06e-03)V_1138 -2.21e-05 1.11e-04 -1.44e-04 1.45e-04 0.694 0.776 0.566 1 1.04e-06
La_V_1210 + V_1210 - (5.772)V_1208 + (8.145)V_1206 - (8.142)V_1202 + (8.175)V_1200 - (5.145)V_1198 + (1.738)V_1196 - (2.07e-03)V_1138 -1.03e-04 2.19e-04 -3.72e-04 3.62e-04 0.618 0.775 0.557 -6 5.03e-06
La_V_1216 + V_1216 - (1.023)V_1214 + (0.013)V_1138 -6.36e-04 1.26e-03 -1.73e-03 1.13e-03 0.814 0.774 0.555 3 7.81e-05
La_V_992 - (1.48e-03)V_1138 + (0.829)V_1004 - (0.808)V_1002 - (1.020)V_994 + V_992 -1.82e-04 1.06e-03 -7.60e-04 7.93e-04 0.052 0.759 0.580 1 4.10e-05
La_V_1004 - (0.026)V_1138 + V_1004 - (0.975)V_1002 -2.06e-04 2.11e-03 -1.62e-03 1.69e-03 0.108 0.756 0.571 7 1.71e-04
La_V_1274 + V_1274 - (1.018)V_1270 + (0.023)V_1226 + (9.05e-04)V_1138 6.12e-04 8.38e-04 1.33e-03 9.44e-04 0.130 0.749 0.544 2 3.74e-05
La_V_886 - (2.30e-04)V_1138 + V_886 - (2.885)V_884 + (2.767)V_882 - (0.881)V_880 - (1.38e-03)V_844 -9.64e-06 3.19e-05 2.09e-05 5.89e-05 0.510 0.743 0.595 -4 1.54e-07
La_V_890 + (3.26e-03)V_1138 + V_890 - (4.805)V_882 + (3.799)V_880 - (3.28e-03)V_844 1.12e-04 8.46e-04 6.94e-04 5.50e-04 0.828 0.741 0.596 -4 3.77e-05
La_V_840 + (0.072)V_1138 + V_840 - (1.106)V_812 3.51e-03 9.94e-03 1.11e-02 6.82e-03 0.786 0.738 0.589 3 5.71e-03
La_V_984 - (0.856)V_1138 + V_984 -8.54e-03 3.09e-02 1.28e-02 1.54e-02 0.423 0.729 0.582 3 3.14e-02
V_908 NA 2.21e-01 1.28e-01 2.61e-01 1.17e-01 0.579 0.596 0.596 NA NA
V_906 NA 2.20e-01 1.27e-01 2.61e-01 1.17e-01 0.585 0.596 0.596 NA NA
V_904 NA 2.20e-01 1.27e-01 2.61e-01 1.17e-01 0.592 0.596 0.596 NA NA
V_892 NA 2.19e-01 1.27e-01 2.61e-01 1.21e-01 0.626 0.596 0.596 NA NA
V_890 NA 2.19e-01 1.27e-01 2.61e-01 1.21e-01 0.616 0.596 0.596 NA NA
V_888 NA 2.19e-01 1.27e-01 2.61e-01 1.22e-01 0.603 0.596 0.596 NA NA
V_912 NA 2.23e-01 1.29e-01 2.63e-01 1.17e-01 0.604 0.595 0.595 NA NA
V_910 NA 2.22e-01 1.28e-01 2.62e-01 1.17e-01 0.587 0.595 0.595 NA NA
V_896 NA 2.20e-01 1.27e-01 2.61e-01 1.20e-01 0.620 0.595 0.595 NA NA
V_894 NA 2.19e-01 1.27e-01 2.61e-01 1.21e-01 0.625 0.595 0.595 NA NA

1.10 Comparing ILAA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA


EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }


pander::pander(table(dataframe[,outcome],pr))
  0 1
0 30 0
1 17 14
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.721 0.592 0.829
3 se 0.452 0.273 0.640
4 sp 1.000 0.884 1.000
6 diag.or Inf NA Inf

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))
  0 1
0 25 5
1 8 23
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.787 0.663 0.881
3 se 0.742 0.554 0.881
4 sp 0.833 0.653 0.944
6 diag.or 14.375 4.108 50.307

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))
  0 1
0 22 8
1 4 27
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.803 0.682 0.894
3 se 0.871 0.702 0.964
4 sp 0.733 0.541 0.877
6 diag.or 18.562 4.931 69.883


par(op)

1.11.1 EFA


  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }


  pander::pander(table(EFAdataframe[,outcome],pr))
  0 1
0 25 5
1 4 27
  pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.852 0.738 0.930
3 se 0.871 0.702 0.964
4 sp 0.833 0.653 0.944
6 diag.or 33.750 8.134 140.031
  par(op)